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Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm (1997)
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| Venue: | IEEE TRANS. SIGNAL PROCESSING |
| Citations: | 366 - 22 self |
BibTeX
@ARTICLE{Gorodnitsky97sparsesignal,
author = {Irina F. Gorodnitsky and Bhaskar D. Rao},
title = {Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm},
journal = {IEEE TRANS. SIGNAL PROCESSING},
year = {1997},
pages = {600--616}
}
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Abstract
We present a nonparametric algorithm for finding localized energy solutions from limited data. The problem we address is underdetermined, and no prior knowledge of the shape of the region on which the solution is nonzero is assumed. Termed the FOcal Underdetermined System Solver (FOCUSS), the algorithm has two integral parts: a low-resolution initial estimate of the real signal and the iteration process that refines the initial estimate to the final localized energy solution. The iterations are based on weighted norm minimization of the dependent variable with the weights being a function of the preceding iterative solutions. The algorithm is presented as a general estimation tool usable across different applications. A detailed analysis laying the theoretical foundation for the algorithm is given and includes proofs of global and local convergence and a derivation of the rate of convergence. A view of the algorithm as a novel optimization method which combines desirable characteristics of both classical optimization and learning-based algorithms is provided. Mathematical results on conditions for uniqueness of sparse solutions are also given. Applications of the algorithm are illustrated on problems in direction-of-arrival (DOA) estimation and neuromagnetic imaging.
Keyphrases
sparse signal reconstruction re-weighted minimum norm algorithm general estimation tool localized energy solution neuromagnetic imaging mathematical result low-resolution initial estimate classical optimization theoretical foundation limited data desirable characteristic learning-based algorithm initial estimate iterative solution integral part dependent variable sparse solution different application local convergence final localized energy solution prior knowledge real signal iteration process detailed analysis focal underdetermined system solver weighted norm minimization novel optimization method nonparametric algorithm
